Dear Basem and Mohammed,
You have presented one of the best essays in the contest. Very clear, modest and not intrusive like many others. You deserve very high rating what you will observe in a minute. However I want to address some issues.
You present important objections to the view No. "2. Mathematics is discovered because it is part of nature just like physics." I agree with all objections if we define math as an abstract language of equations. Then the answer is No.3. The mathematics is invented as an abstract, platonic language used to describe reality and also for many other purposes. But pure geometry, in the meaning of shape and its dynamics and not equations or human language, is discovered in the sense that we perceive shapes and its dynamical changes. I think we need an universal, visual language, based on that geometry. It would be comprehensible to future supercomputers, aliens and maybe children as well. So far we have to use equations as our deficient language.
You claim: "...Mathematics is structured as theorems based on axioms. Axioms are the premise or starting point on which we build theorems" As you probably know, there were many attempts to formulate axioms also in physics (D. Hilbert, J. von Neumann, L. Nordheim, H. Weyl, E. Schrödinger, P. Dirac, E. P. Wigner and others). All these efforts failed. That is a pity, however a deductive system can consist not only of axioms but also other, already established theorems. So far theorems were reserved exclusively for mathematics. That means that we can use these established theorems only if we accept that the reality is isomorphic to mathematical structures. You argue that it is not the case and I agree. But we can use geometrical structures instead general notion of mathematical ones. Then we could try e.g. with the geometrization conjecture, proved by Perelman (so it is a theorem). And it generates testable predictions what you demand in conclusions. We have the set of 8 Thurston geometries. We can treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime. Then we use the correspondence rule to assign interactions and matter to the proper geometries. It seems to be oversimplified but you can find some technicalities in e.g. Torsten Asselmeyer-Maluga and Helge Rose's publications (arxiv.org/abs/1006.2230, arxiv.org/abs/1006.2230v6). In details it is really complicated.
If you are interested you can take a look at my essay.
I would appreciate your comments however I would understand if you were tired with the contest.
Jacek